Questions tagged [tolerance-interval]
A tolerance interval is an interval that contains $p\%$ of a population with $(1-\alpha)$ confidence. A TI is distinct from (but sometimes confused with) prediction intervals & confidence intervals.
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Translation of Stange's (1971) approach to tolerance limits in simple linear regression
In Stange (1971), Angewandte Statistik, Vol. II. Springer Verlag, Berlin, Heidelberg,
New York, 141-143, the author derives a tolerance limit for simple linear regression which is widely used in ...
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Extreme value function in R
I have a small data set (n=25) with an unknown distribution and I'm trying to find a distribution function that is as similar as possible in order to ultimately determine tolerance limits. I used the ...
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Linear Model + tolerance intervals: How to show that when a condition is fulfilled for a tool it is also fulfilled for another related tool?
The problem
Imagine that you have two different tools that produce data at given time points $t_1,...,t_m$. Suppose that we only have access to the mean and standard deviation of the data at each time ...
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When to pool batches for tolerance intervals?
Imagine that we have at disposal several batches of data from a given process and that the interval time of record of each batches can be week, months or even years.
Out of these data, we would like ...
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Calculation of a nonparametric equal-tailed (central) tolerance interval for an unknown continuous distribution
Assume we have a sample of size $n$ from an unspecified continuous distribution $F(\cdot)$. We wish to construct a tolerance interval to contain $(100\,\beta)\%$ of the population with a pre-specified ...
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Bootstrapping with quantiles of data instead of SD*z?
I have recently been bootstrapping the confidence intervals of a neural network model estimated to data.
I execute the following psudo-code, which seems similar to previous bootstraps I have done:
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Conditional Tolerance Interval
With the generous help of people here, I've recently learned about the notion of a Tolerance Interval (Confidence in a range estimate, and +- 2sigma rule of thumb).
I am now working on an application ...
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Prediction Intervals and Tolerance Intervals [duplicate]
I have a question regarding interpretation of prediction intervals and confidence intervals. The definitions I've seen is:
(1) A prediction interval for a single future observation is an interval ...
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How does the Empirical Rule align with Tolerance Interval
For Empirical Rule, 95% of the observed data will occur within the second standard deviation, but what is the difference between this and the 95/95 2-sided tolerance interval ? It includes 95% of ...
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Lower confidence with larger sample size? Tolerance interval for distribution-free data
I am trying to find the sample size required in order to establish a tolerance interval which contain 99% of the population, with 95% confidence. The results from Minitab for a sample size of 473 are ...
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Is it possible to estimate a specific quantile of a prediction based on the results of ordinary linear regression?
We can estimate mean value of a prediction with a specific confidence, we have an estimated value of a variance (MSE) and we also assume that prediction is a normally distributed random variable. Isn'...
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interval depending on sample size
I came across these funnel plots here and tried to reproduce something similar where I have a normally distributed population and I happen to know the true population mean (500000) and standard ...
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Tolerance Interval from the posterior predictive distribution of a ratio of two Normal distributions
I am trying to calculate a Beta-Gamma Tolerance Interval from the Posterior Predictive Distribution of a log(ratio) of two normal (no close form available).
In the minimal R code below, assume ...
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tolerance interval, sample size and power
I can only find limited information on how to calculate sample sizes in respect to tolerance intervals. I have a particular problem I would appreciate any help on.
If I had a normally distributed ...
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How to set the tolerance in Gradient descent?
I understand that one solution of setting the number of iterations, is to set it to a large number and then interrupt it when the gradient vector becomes tiny, so tiny that it is smaller than a ...
